You can defer the installation of the updates until after the installation. Then via package updater, you can see the packages to be updated. Underneath the list of packages, you will see the total amount of data to be downloaded stated in MBs :)

The answer to this question will vary a lot. You can as pointed out by other answers you can install Ubuntu without a working internet connection so the answer is zero.

But if you choose to let it update as its installing which many people do then it will download the updates to the packages you have since the DVD image was produced. The older the image the more updates there are likely to be.

If you do decide to install offline then Ubuntu will download all the updates the first time you run Update Manager.

Assuming you want to know how much data is downloaded and also assuming you are installing Ubuntu while connected to the Internet (Not offline) then the amount will vary depending on the following:

What language you are using for Ubuntu. If you are using English then only the data for English will be downloaded (apart from any other updates needed). If you are using French, Spanish, Chinese or any other language, the size of the data will increase or decrease depending on the size of the language packs needed.

How long since the official release are you installing Ubuntu. If you are installing Ubuntu the same day that specific version was released, the amount of updates will be minimal. If however, you are installing Ubuntu 6 months after it was released, you will get 6 months worth of updates. This can vary a lot. From 200 MB worth of updates to 700 MB. I once got 1.1 GB of updates when I tried installing a LTS a 14 months after it was released.

Which version of Ubuntu you are installing. Since 12.04, versions of Ubuntu have slowly but surely lowered the amount of data needed for upgrades. The size of many packages have lowered. So it is not the same to update 11.10 than to update 13.04.

Which Ubuntu distro you are using. Ubuntu alone has an amount of packages that will need to update after a certain amount of time. If you have KDE, it would need a bit more. Same goes for other official distros based on Ubuntu. They would have to download, not only the core components found on the Ubuntu repositories, but also the packages needed for the Desktop system (KDE packages for Kubuntu, LXDE packages for Lubuntu...)

So in general, depending on the time of release, the delta between installation time and release time, the Ubuntu version and the Ubuntu distro you will have to download data sizes that can change from 1 KB to 1 GB (Am exaggerating with the 1 GB but the point being that it varies a lot).